All you are trying to do when you re-distill your spirit is to separate the alcohol in the spirit from any solids. Your main goal is to distill ALL the ethanol from the spirit and leave only solids and water behind in the proofing still. Once you extract the ethanol then you add only pure water to your distillate to get back to your original volume that you distilled (before adding any extra water to rinse the flask). Then you can take the proof with hydrometers and that will tell you the proof of your original spirit. The extra water to rinse the flask will not change the amount of ethanol you will distill.
Example: Start with 500ml of your sweetened spirit. Assume all volume and proof readings are taken at 60F! Make sure all 500ml gets into the still and use XXml of rinse water if needed. Distill until you have collected all ethanol, (until still temp is at 212F). Stop distillation and add XXml of water to get the distillate volume back to 500ml exactly. Now you've effectively replaced the solids in the spirit with just water but it has the same ethanol content and volume as your original sample. Proof distillate with hydrometers.
The key is to make sure you get all the ethanol out so you must make sure all the spirit gets into the proofing still and you also don't lose any through evaporation while distilling or you'll be under proof.